Air carrier First Officer reported a GPWS Terrain warning while on the ELP RNAV RNP Z 26L approach. The pilots believe the aircraft was on path and the warning did not coincide with the aircraft's position. During descent the crew stated they had also received a momentary GPS fail indication.

Narrative

On short approach in VMC just below approx 500 feet AGL into El Paso Runway 26L we got a 'CAUTION; TERRAIN' GPWS caution followed by GPWS warning; 'TERRAIN; TERRAIN; PULL UP'. Captain immediately executed terrain avoidance maneuver. We followed Tower heading and altitude assignment and then switched to Departure Control frequency. Captain engaged autopilot repeatedly followed by repeated disengagements making communications difficult due to constant aural warning. This created an additive condition. Assigned heading was to the left with the autopilot commanding right turns upon autopilot engagement. Captain made appropriate corrections and we commenced an ILS approach to Runway 22 without further incident.It was difficult to ascertain why we received the GPWS warning as we believed we were on profile for the RNAV RNP Z 26L Approach; however; upon descent for approach we had received a spurious and temporary GPS-L fail message. We speculated that it may have been possible both GPS sensors failed due to potential military activities in the area which could have caused the GPWS warning. The terrain displayed on MFD was sudden and not concurrent with actual terrain situation.More attention to NOTAMs may have given pause to attempting a GPS approach and steered us toward conducting an ILS type approach.Go-around caused by GPWS.